As a transmission of a vehicle, a mechanical automatic transmission in which a torque converter is not used is known. In the mechanical automatic transmission, operation (select and shift) of a gearbox and disconnection and connection of a clutch in a manual transmission are actuated by an actuator to enable automatic gear shifting that does not require a torque converter. In the transmission, for example, as described in Patent Literature 1, a gear group fixedly provided in a first or a second input shaft coaxial with a crankshaft of an engine and a gear group supported by a sub-shaft or an output shaft and connected to the respective shafts by a meshing clutch mechanism are meshed with each other, a driving force input from the engine is shifted, and the shifted driving force is output from the output shaft.